課程名稱︰普通物理學 課程性質︰化工系定必修 課程教師︰趙治宇 開課學院：理學院 開課系所︰物理系開給化工系 考試日期（年月日）︰99/06/24 考試時限（分鐘）：10:20~13:10(170分鐘) 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. Describe briefly (a) the evidence of the universe expansion and (b) the working principle cooling invested by Steven Chu. (4%,6%) 2. What's the working principle of tape recording and playback in a video tape recorder. (4%,4%) 3. Design a experiment to show the existence of diamagnetic material. (8%) 4. What's the operating principle of polymer chain reaction (PCR)? (10%) 5. Describe (a) the behavior of electric field of partially polarized light, and (b) what's the difference between unpolarized light and circularly polarized light. (3%,6%) 6. Figure 1 shows a coil of N_2 turns wound as shown around part of a toroid of N_1 turns. The toroid's inner radius is a, its outer radius is b, and its height is h. Show that the mutual inductance M for the toroid-coil combination is given by μ_0 N_1 N_2 h b M=-------------- ln--- (8%) 2π a (不會畫圖(￣□￣|||)a) 7. A square loop of wire of edge length a carries current i. Show that the magnitude of the magnetic field produced at a point on the central perpendicular axis of the loop and a distance x from its center is. 4 μ_0 i a^2 B=-------------------------------- (8%) π(4X^2 + a^2)(4X^2 + 2a^2)^1/2 8. In Fig. 2, after switch S is closed at time t = 0, the emf of the source is automatically adjusted to maintain a constant i through S. (a) Find the current through the inductor as a function of time. (b) At what time is the current through the resistor equal to the current through the inductor? (4%,4%) S ┌﹨─┬┐ constant- ││ current R L source- ││ └──┴┘ 9. The fractional half-eidth Δω_d of a resonance curve, such as the ones in Fig.3, is thw width of curve at half the maximum value of I. Show that Δω_d /ω = R(3C/L)^ 1/2, where ω is the angular frequency at resonance. Note that the ratio Δω_d / ω increases with R, as Fig. 3 shows. (8%) (太複雜了......不好意思我不會畫) 10. Consider a solid containing N atoms unit volume, each atom having a magnetic dipole moment (頭上有→)μ. Suppose the direction of (頭上有→)μ can be only parallel or antiparallel to an externally applied magnetic field (頭上有→)B (This will be the case if (頭上有→)μ is due to the spin of a single electron). According to statistical mechanics, the probability of an atom being in a state with energy U is proportional to e^(-U/kt), where T is the temperature and k is Boltzmann's constant. Thus, because energy U is -(頭上有→)μ * (頭上有→)B, the fraction of atoms whose dipole moment is antiparallel to e^ (μB/kT) and the fraction of atoms whose dipole moment is antiparallel to (頭上有→)B is proportional to e^(μB/kT). Show that the magnitude of the magnetization of this solid is M = Nμtanh(μB/kT). (8%) 11. In Fig 4, a microwave transmitter at height a above the water level of a wide lake transmits microwaves of λtoward a receiver on the opposite shore, a distance x above the water level. The microwaves reflecting from the water interfere with the microwaves arriving directly from the transmitter. Assuming that the lake width D is much greater than a and x, and that λ >= a, find an expression that gives the values of x for which the signal at the receiver is maximum. (8%) ( Hint: Does the reflection cause a phase change? ) ▃─ ▎↑a ─▂ ▎↓ x│ ▏ ======================== │------------------▏ D 12. Assume that the limits of the visible spectrum are arbitrary chosen as 430 and 680 nm. Calculate the number of rulings per millimeter of a grating that will spread the first order spectrum through an angle of 20.0度. (7%) --

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